A038157 a(n) = n! * Sum_{k=1..n-2} 1/k!.

0, 0, 0, 6, 36, 200, 1230, 8652, 69272, 623520, 6235290, 68588300, 823059732, 10699776672, 149796873590, 2246953104060, 35951249665200, 611171244308672, 11001082397556402, 209020565553571980, 4180411311071439980, 87788637532500240000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..449
• Index entries for sequences related to factorial numbers

Programs

Mathematica

a=1;Table[a=(a-n)*(n+1);Abs[a],{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Nov 20 2009 *)
Table[n!Sum[1/k!,{k,n-2}],{n,0,30}] (* Harvey P. Dale, Dec 26 2021 *)

Formula

a(n) = floor(n!*exp(1)) - n - 1 - n! for n>1. - Mark van Hoeij, Oct 30 2011